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Abstract We examine the geometrical differences between the black hole (BH) and naked singularity (NS) or superspinar via Lense–Thirring (LT) precession in spinning modified-gravity (MOG). For BH case, we show that the LT precession frequency ( $$\Omega _{LT}$$ Ω LT ) along the pole is proportional to the angular-momentum (J) parameter or spin parameter (a) and is inversely proportional to the cubic value of radial distance parameter, and also governed by Eq. (1). Along the equatorial plane it is governed by Eq. (2). While for superspinar, we show that the LT precession frequency is inversely proportional to the cubic value of the spin parameter and it decreases with distance by MOG parameter as derived in Eq. (3) at the pole and in the limit $$a>>r$$ a > > r (where a is spin parameter). For $$\theta \ne \frac{\pi }{2}$$ θ ≠ π 2 and in the superspinar limit, the spin frequency varies as $$\Omega _{LT}\propto \frac{1}{a^3\cos ^4\theta }$$ Ω LT ∝ 1 a 3 cos 4 θ and by Eq. (38).

Introduction: Research has shown that learning may be optimised by synchronising the learning environment with the learning style preferences of students. First-year medical students face immense stress as they adapt to a new learning environment and curriculum at the onset of their medical career. The simultaneous use of two supplementary learning styles questionnaires, namely, the Visual-Aural/Auditory-Read/Write-Kinesthetic (VARK) questionnaire and the Vermunt Inventory of Learning Styles (Vermunt ILS), would provide detailed knowledge of their instructional preferences, information processing, and cognitive personality learning styles. Judicious use of such information at this stage may guide them towards improved learning and higher academic achievement. Aim: To study the association between learning styles and academic achievements in first-year professional MBBS students of a medical college. Materials and Methods: A cross-sectional study was conducted at Medical College, Kolkata, West Bengal, India over the duration of 10 months from August 2021 to June 2022. Online surveys of 250 first-year MBBS students’ learning styles were conducted using the VARK questionnaire and Vermunt ILS, and the marks of three internal assessment examinations were collected. The data was entered into Microsoft Excel. Group as well as individual scores were analysed, and Pearson’s Chi-square test was used to determine the association between the students’ learning styles and their academic achievement. A p-value of

Background: Complete hydatidiform mole affects women in their reproductive age. About 15-20% develops persistent molar gestational trophoblastic neoplasia (GTN), which is linked with delayed (beyond 56 days) normalization of serum βHCG after surgical evacuation. Objective: The objective of the article is to shorten the duration of normalization time of βHCG with single-dose methotrexate injection in women with high risk complete hydatidiform mole (CHM) after suction evacuation. Methods: Total 76 women with CHM were randomized into intervention and control groups. In the intervention arm (n = 34) women received single dose 100 mg intramuscular methotrexate injection post evacuation and the control group (n = 42) had standard care. Surveillance was done in both groups at two weeks intervals for next six months and duration of normalization of βHCG level was recorded. Results: Total 94.7% women completed follow-up. Mean of normalization time was significantly lower in the intervention group compared to controls (9.7 weeks versus 14.7 week; P < 0.01). Time to event curve showed significantly earlier cumulative normalization time for the intervention group. Conclusion: Single-dose 100 mg methotrexate injection is a low-cost, simple intervention to help one out of three women with CHM with high-risk features to achieve normalization of βHCG within 56 days. This might be helpful for people in resource-poor countries where adherence to prolonged surveillance is poor.

Background and Objectives: The enigma COVID-19 pandemic already involved major parts of globe with toll of 2,074,529 victims and 139,378 deaths from 213 countries/territories as on April 14, 2020. It cripples nations by the loss of human resources, economic decline, hunger, unemployment insecurities giving way to mental morbidities, and still many others to be discovered. Till it completes its trajectory, a systematic investigation, a prerequisite of any epidemic control, is warranted. Materials and Methods: A cross-sectional survey over 2 weeks (April 15, 2020–April 28, 2020) has been conducted at a teaching institution at Kolkata aiming to describe the magnitude, pattern, severity, and correlates of coronavirus pandemic 2020. Data pertaining to COVID-19 cases, deaths of affected countries, and their reported and or potential correlates were retrieved from various public domains, for example, https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports, worldpopulationreview.com, data.worldbank.org. Results: Multiple linear regression analysis revealed a maximum R2 of 32.3% (P = 0.013) with a significant model fit (P = 0.000) for COVID-19 incidence rate per million which is associated positively with the proportion of the urban population (b = 0.024) and the percentage of the population aged 65 years or higher (b = 0.112) and negatively with current universal Bacille Calmette-Guérin vaccination (b = −1.021) policy of countries. Conclusion: Against this viral catastrophe evidence-based classical public health measures are underway. Notwithstanding variations in testing and reporting policy, the findings of this research ignite further study.

Abstract We investigate the energy extraction by the Penrose process in Kerr-MOG black hole (BH). We derive the gain in energy for Kerr-MOG as $$\begin{aligned} \varDelta {{\mathcal {E}}} \le \frac{1}{2}\left( \sqrt{\frac{2}{1+\sqrt{\frac{1}{1+\alpha }-\left( \frac{a}{{{\mathcal {M}}}}\right) ^2}} -\frac{\alpha }{1+\alpha } \frac{1}{\left( 1+\sqrt{\frac{1}{1+\alpha }-\left( \frac{a}{{{\mathcal {M}}}}\right) ^2} \right) ^2}}-1\right) \end{aligned}$$ ΔE≤1221+11+α-aM2-α1+α11+11+α-aM22-1 where a is spin parameter, $$\alpha $$ α is MOG parameter and $${{\mathcal {M}}}$$ M is the Arnowitt–Deser–Misner (ADM) mass parameter. When $$\alpha =0$$ α=0 , we obtain the gain in energy for Kerr BH. For extremal Kerr-MOG BH, we determine the maximum gain in energy is $$\varDelta {{\mathcal {E}}} \le \frac{1}{2} \left( \sqrt{\frac{\alpha +2}{1+\alpha }}-1 \right) $$ ΔE≤12α+21+α-1 . We observe that the MOG parameter has a crucial role in the energy extraction process and it is in fact diminishes the value of $$\varDelta {{\mathcal {E}}}$$ ΔE in contrast with extremal Kerr BH. Moreover, we derive the Wald inequality and the Bardeen–Press–Teukolsky inequality for Kerr-MOG BH in contrast with Kerr BH. Furthermore, we describe the geodesic motion in terms of three fundamental frequencies: the Keplerian angular frequency, the radial epicyclic frequency and the vertical epicyclic frequency. These frequencies could be used as a probe of strong gravity near the black holes.

We compute area (or entropy) product formula for Newman-Unti-Tamburino (NUT) class of black holes. Specifically, we derive the area product of outer horizon and inner horizon (H±) for Taub-NUT, Euclidean Taub-NUT black hole, Reissner-Nordström–Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT black hole under the formalism developed very recently by Wu et al. (2019) [1]. The formalism is that a generic four dimensional Taub-NUT spacetime should be described completely in terms of three or four different types of thermodynamic hairs. They are defined as the Komar mass (M=m), the angular momentum (Jn=mn), the gravitomagnetic charge (N=n), the dual (magnetic) mass (M˜=n). After incorporating this formalism, we show that the area (or entropy) product of both the horizons for NUT class of black holes are mass-independent. Consequently, the area product of H± for these black holes are universal. Which was previously known in the literature that the area product of said black holes are mass-dependent. Finally, we can say that this universality is solely due to the presence of new conserved charges JN=MN which is closely analogue to the Kerr like angular momentum J=aM.

A correction to this paper has been published: 10.1140/epjc/s10052-016-3976-1

We have examined the thermodynamic volume products for spherically symmetric and axisymmetric spacetime in the framework of extended phase space. Such volume products are usually formulated in terms of the outer horizon (H+) and the inner horizon (H-) of black hole (BH) spacetime. Besides volume product, the other thermodynamic formulations like volume sum, volume minus, and volume division are considered for a wide variety of spherically symmetric spacetime and axisymmetric spacetime. Like area (or entropy) product of multihorizons, the mass-independent (universal) features of volume products sometimes also fail. In particular, for a spherically symmetric AdS spacetime, the simple thermodynamic volume product of H± is not mass-independent. In this case, more complicated combinations of outer and inner horizon volume products are indeed mass-independent. For a particular class of spherically symmetric cases, i.e., Reissner Nordström BH of Einstein gravity and Kehagias-Sfetsos BH of Hořava Lifshitz gravity, the thermodynamic volume products of H± are indeed universal. For axisymmetric class of BH spacetime in Einstein gravity, all the combinations are mass-dependent. There has been no chance to formulate any combinations of volume product relation to be mass-independent. Interestingly, only the rotating BTZ black hole in 3D provides that the volume product formula is mass-independent, i.e., universal, and hence it is quantized.

We examine the thermodynamic properties of inner and outer horizons in the background of Hořava–Lifshitz black hole. We compute the horizon radii product, the surface area product, the entropy product, the surface temperature product, the Komar energy product and the specific heat product for both the horizons. We show that surface area product, entropy product and irreducible mass product are universal (mass-independent) quantities, whereas the surface temperature product, Komar energy product and specific heat product are not universal quantities because they all depend on mass parameter. We further study the stability of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses second order phase transition.

We examine the logarithmic corrections to the black hole (BH) entropy product formula of outer horizon and inner horizon by taking into account the effects of statistical quantum fluctuations around the thermal equilibrium and via conformal field theory (CFT). We argue that, in logarithmic corrections to the BH entropy product formula when calculated using CFT and taking into account the effects of quantum fluctuations around the thermal equilibrium, the formula should not be universal and it also should not be quantized. These results have been explicitly checked by giving several examples.

We investigate the entropy product formula for various gravitational instantons. We speculate that due to the mass-independent features of the said instatons they are universal as well as quantized. For isolated Euclidean Schwarzschild black hole, these properties simply fail.

It has been shown by explicit and exact calculation that the geometric product formula i.e., area (or entropy) product formula of outer horizon ( H + ) and inner horizon ( H − ) for charged accelerating black hole (BH) should neither be mass-independent nor quantized. This implies that the area (or entropy ) product is mass-independent conjecture has been broken down for charged accelerating BH. This also further implies that the mass-independent feature of the area product of H ± is not a generic feature at all. We also compute the Cosmic-Censorship-Inequality for this BH. Moreover, we compute the specific heat for this BH to determine the local thermodynamic stability. Under certain criterion, the BH shows the second order phase transition. Furthermore, we compute logarithmic corrections to the entropy for the said BH due to small statistical fluctuations around the thermal equilibrium.

We derive thermodynamic product relations for four-parametric regular black hole (BH) solutions of the Einstein equations coupled with a nonlinear electrodynamics source. The four parameters can be described by the mass (m), charge (q), dipole moment (α), and quadrupole moment (β), respectively. We study its complete thermodynamics. We compute different thermodynamic products, that is, area product, BH temperature product, specific heat product, and Komar energy product, respectively. Furthermore, we show some complicated function of horizon areas that is indeed mass-independent and could turn out to be universal.

We investigate the comprehensive geodesic structure of a spherically symmetric, static charged regular Ayón-Beato and García black hole (BH). We derive the equation of innermost stable circular orbit (ISCO), marginally bound circular orbit (MBCO) and circular photon orbit (CPO) of said BH, which are most relevant to BH accretion disk theory. Using time-like geodesic properties, we derive Paczyński-Witta potential form for this BH which are very relevant to determine the general relativistic effects on the accretion disk. We show that at a certain radius (For example in case of Reissner-Nordstrøm (RN) BH, r ∗ = Q 2 M ), there exists zero angular momentum (ZAM) orbits due to the repulsive gravity. We also show that in the eikonal approximation, the real and imaginary parts of the quasi normal modes (QNM) of the regular BHs can be expressed as in terms of the frequency of the BH and the instability time scale of the unstable null circular geodesics. Moreover, we study the Bañados, Silk and West effect for this BH. We show that the center-of-mass (CM) energy of colliding neutral test particles near the infinite red-shift surface of the regular BHs have the finite energy. In the Appendix section, we have discussed the possibility of a regular ABG BH can act as particle accelerators when two charged test particles of different energies are colliding and approaching to the horizon of the BH provided that one of charged test particle has a critical value of charge.

We investigate the thermodynamics and phase transition for Kiselev black hole and dilaton black hole. Specifically we consider Reissner-Nordström black hole surrounded by radiation and dust and Schwarzschild black hole surrounded by quintessence, as special cases of Kiselev solution. We have calculated the products relating the surface gravities, surface temperatures, Komar energies, areas, entropies, horizon radii, and the irreducible masses at the Cauchy and the event horizons. It is observed that the product of surface gravities, product of surface temperature, and product of Komar energies at the horizons are not universal quantities for the Kiselev solutions while products of areas and entropies at both the horizons are independent of mass of the above-mentioned black holes (except for Schwarzschild black hole surrounded by quintessence). For charged dilaton black hole, all the products vanish. The first law of thermodynamics is also verified for Kiselev solutions. Heat capacities are calculated and phase transitions are observed, under certain conditions.

We derive the thermodynamic products, in particular the area (or entropy) products of H ± for a wide variety of black holes (BHs) in anti-de Sitter (AdS) space. We show by explicit and exact calculations that, for this class of BHs, more complicated functions of the event horizon area and Cauchy horizon area are indeed mass-independent. This mass-independent results indicate that they could turn out to be a “universal” quantity provided that they depend only on the quantized angular momentum, quantized charges, and cosmological constant, etc. Furthermore, these area (or entropy) product relations for several classes of BHs in AdS space gives us strong indication to understanding the nature of non-extremal BH entropy (both inner and outer) at the microscopic level. Moreover, we compute the famous Cosmic Censorship Inequality (which requires Cosmic-Censorship hypothesis) for these classes of BHs in AdS space. Local thermodynamic stability has been discussed for these BHs and under certain conditions, these classes of BHs displayed second order phase transition. The super-entropic BH does not provide any kind of second order phase transition.