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In a recent paper, Raju showed that the essential features of the monogamy paradox for old flat space black holes could be modeled using a setup in empty AdS, leading to a violation in the monogamy of entanglement there. A physically interesting question is whether such a violation in the monogamy of entanglement can be posed in empty flat space. The answer is not immediately clear since flat space gravity has an entirely different vacuum and infrared structure than the gapped and unique AdS vacuum, which was exploited in Raju's toy model. We answer this question in the affirmative, with an explicit construction. We formulate the paradox in terms of monogamy of CHSH correlations, which we use to quantify the monogamy of entanglement. Extending Raju's analysis to empty flat space, within effective field theory, we show that the entanglement of approximately local bulk modes just outside a light cone with modes just inside the light cone as well as with modes situated far away at the past of future null infinity gives rise to an O($1$) violation in the monogamy of entanglement. This cannot be resolved by small corrections of O($\sqrt{G_N}$). The issues arising from the above-mentioned vacuum and infrared features unique to flat spacetime are dealt with by introducing a physically motivated boundary projector onto states below a given infrared cutoff, which allows us to construct suitable operators at the past of future null infinity that give rise to the violation. We argue that the resolution of the paradox is that our spatially separated observables probe the same underlying degrees of freedom, i.e., such observables act on a non-factorized Hilbert space arising from the Gauss constraint, thereby circumventing the conflict with monogamy of entanglement., Minor restructuring of abstract and introduction

Observations show that the expansion of the Universe is accelerating. This requires that the dominant constituent of matter in the Universe has some unusual properties like negative pressure. This exotic component has been given the name dark energy. We work with the simplest model of dark energy, the cosmological constant introduced by Einstein. We study the evolution of spherical over-densities in such a model and show that there is a minimum over-density required for collapse: perturbations with a smaller amplitude do not collapse. This threshold is interesting as even perturbations with a positive over-density and negative energy do not collapse in finite time. Further, we show that perturbations with an amplitude larger than, but comparable to the threshold value, take a very long time to collapse. We compare the solutions with the case when dark energy is absent., Comment: 17 pages, 7 figures. Accepted for publication in Resonance, journal of science education

Departures from standard spherically symmetric solar models, in the form of perturbations such as global and local-scale flows and structural asphericities, result in the splitting of eigenfrequencies in the observed solar spectrum. Here we describe new theoretical developments that enable the computation of sensitivity kernels for frequency splittings (a coefficients) due to general Lorentz stresses in the Sun. We draw from theoretical ideas prevalent in normal-mode coupling theory in geophysical literature to build these kernels. We plot the Lorentz-stress kernels and estimate the a-coefficients arising from a combination of deep-toroidal and surface-dipolar fields (although we note that this could equally well be substituted by another choice of Lorentz stresses). These results pave the way to formally pose an inverse problem, and infer magnetic fields from the measured even a-coefficients.

Departures from standard spherically symmetric solar models, in the form of perturbations such as global and local-scale flows and structural asphericities, result in the splitting of eigenfrequencies in the observed spectrum of solar oscillations. Drawing from prevalent ideas in normal-mode coupling theory in geophysical literature, we devise a procedure that enables the computation of sensitivity kernels for general Lorentz stress fields in the Sun. Mode coupling due to any perturbation requires careful consideration of self- and cross-coupling of multiplets. Invoking the isolated-multiplet approximation allows for limiting the treatment to purely self-coupling, requiring significantly less computational resources. We identify the presence of such isolated multiplets under the effect of Lorentz stresses in the Sun. Currently, solar missions allow precise measurements of self-coupling of multiplets via "$a$-coefficients" and the cross-spectral correlation signal which enables the estimation of the "structure coefficients". We demonstrate the forward problem for both self-coupling ($a$-coefficients) and cross-coupling (structure coefficients). In doing so, we plot the self-coupling kernels and estimate $a$-coefficients arising from a combination of deep-toroidal and surface-dipolar axisymmetric fields. We also compute the structure coefficients for an arbitrary general magnetic field (real and solenoidal) and plot the corresponding "splitting function", a convenient way to visualize the splitting of multiplets under 3D internal perturbations. The results discussed in this paper pave the way to formally pose an inverse problem, and infer solar internal magnetic fields., 32 pages, 8 figures, Astrophysical Journal