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Abstract:We consider the quantum vacuum effects of the massless scalar fields that are non-minimally coupled to the background geometry of a collapsing homogeneous ball of dust. It is shown that for a definite range of coupling constants, there are repulsive quantum vacuum effects, capable of stopping the collapse process inside the black hole and precluding the formation of singularity. The final fate of the collapse will be a black hole with no singularity, inside which the matter stays balanced. The density of the final static matter will be close to the Planck density. We show that the largest possible radius of the stable static ball inside a black hole with Schwarzschild mass M is given by 1 90π M mp 1 3 p . If the black hole undergoes Hawking radiation, the final state will be an extremal quantumcorrected black hole, with zero temperature, with a remnant of matter inside. We show that the resolution of singularity is not disrupted under Hawking radiation.

Galaxy power spectrum and bispectrum signals are distorted by peculiar velocities and other relativistic effects arising from a perturbed spacetime background. In addition, study of correlation functions of tracers in Fourier space is often done in the plane-parallel approximation under which it is assumed that line-of-sight vectors are parallel. In this work we show that a simple perturbative procedure can be employed for a fast evaluation of beyond plane-parallel (wide-angle) corrections to the power spectrum and bispectrum. We also show that evolution of linear matter density fluctuations in a relativistic context can be found from a simple method. For the power spectrum at linear level, we compare leading order wide-angle contributions to multipoles of the galaxy power spectrum with those from non-integrated and integrated relativistic corrections and estimate their possible contamination on local fNL measurements to be of order a few. We also compute wide-angle corrections in the presence of nonlinear terms at one-loop order. For the bispectrum, we show that wide-angle effects alone, even with fully symmetric choices of LOS, give rise to imaginary, oddparity multipoles of the galaxy bispectrum (dipole, octupole, etc.) which are in many cases larger than previously known ones of relativistic origin. We calculate these contributions and provide an estimator for measuring the leading order bispectrum dipole from data, using a symmetric LOS definition. Finally, we calculate the leading order corrections to multipoles of real plane-parallel bispectrum multipoles and estimate the apparent local fNL induced to be of order unity.