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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2021

Modified Schwarzschild metric from a unitary accelerating mirror analog

We present a modified Schwarzschild solution for a model of evaporation of a black hole with information preservation. By drawing a direct analogy to the quantum pure accelerating mirror (dynamical Casimir effect of a 1D horizon), we derive a Schwarzschild metric with not only the usual Schwarzschild radius but an additional length scale related to the Planck length. The black hole has thermal particle production that leads to complete evaporation of the black hole, resulting in non-divergent entanglement entropy, Page curve turn-over, and an asymptotic quantum pure state with no information loss.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole

The interior of a static Schwarzschild metric can be written in terms of two functions, similar to some models of anisotropic cosmology. With a suitable choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW) inside the horizon of a Schwarzschild black hole. By imposing classicality near the horizon, and requiring boundedness of the wave function, we get a rather generic solution of the WDW equation, whose steepest-descent solution, i.e., the ridge of the wave function, coincides nicely with the classical trajectory. However, there is an ambiguity in defining the arrow of time which leads to two possible interpretations—(i) if there is only one arrow of time, one can infer that the steepest-descent of the wave function follows the classical trajectory throughout: coming from the event horizon and going all the way down to the singularity, while (ii) if there are two different arrows of time in two separate regimes, it can be inferred that the steepest-descent of the wave function comes inwards from the event horizon in one region while it moves outwards from the singularity in the other region, and there exists an annihilation process of these two parts of the wave function inside the horizon. Additionally, adopting the second interpretation could shed light on the information loss paradox: as time goes on, probabilities for histories that include black holes and singularities decay to zero and eventually only trivial geometries dominate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Leptodermic corrections to the TOV equations and nuclear astrophysics within the effective surface approximation

The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of the Schwarzschild metric in the spherical case are found with these surface corrections to the known leading (zero) order of the leptodermic approximation a/R << 1, where a is the NS effective-surface (ES) thickness, and R is the effective NS radius. The energy density $\mathscr{E}$ is considered in a general form including the functions of the particle number density and of its gradient terms. The macroscopic gravitational component $Φ$(ρ) of the energy density is taken into account in the simplest form as expansion in powers of $ρ$ – $\overline{ρ}$, where $\overline{ρ}$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions ρ across the NS ES in the normal direction to the ES, which are derived in the simple analytical form at the same leading approximation, was used for the derivation of the modified TOV (MTOV) equations by accounting for their NS surface corrections. As a result, the MTOV equations are analytically solved at first order and the results are compared with the standard TOV approach of the zero order.

Magner, A. G. [Institute for Nuclear Research, Kyi↗
DOE OSTI2021

Embedding condition describing shearing, dissipative collapse

Highlights: • Perturbative approach to the time-dependent Karmarkar condition in shearing collapse. • Analysis of the (in)stability of the collapsing fluid using the TOV equation. • Study of the temperature profiles using a causal heat transport equation. In this work we employ the time-dependent Karmarkar condition to model dissipative gravitational collapse in the presence of shear which leads to a final static configuration. We believe that this is a first attempt at using the time-dependent Karmarkar condition describing a radiating star with shear in which the collapsing core dissipates energy in the form of a radial heat flux. The final static configuration which is described by an embedding class I spacetime was obtained by Hansraj and Moodly who showed that this solution satisfies all the physical requirements for a static compact object. As the collapse proceeds and the heat flux tends to zero the dynamical core evolves into a static compact core with the exterior spacetime being described by the vacuum Schwarzschild solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quasinormal modes and shadow of a Schwarzschild black hole with GUP

Highlights: • The physics of quantum corrected Schwarzschild Black Hole via GUP is investigated. • Quasinormal Modes (QNM) are obtained via WKB and numeric methods. • The relationship between shadow and QNM in the eikonal limit is established. • The quadratic and linear GUP parameters affect the results in a clear way. We consider quantum corrections for the Schwarzschild black hole metric by using the generalized uncertainty principle (GUP) to investigate quasinormal modes, shadow and their relationship in the eikonal limit. We calculate the quasinormal frequencies of the quantum-corrected Schwarzschild black hole by using the sixth-order Wentzel–Kramers–Brillouin (WKB) approximation, and also perform a numerical analysis that confirms the results obtained from this approach. We also find that the shadow radius is nonzero even at very small mass limit for finite GUP parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Four metrics

A central idea in general relativity is that physics should not depend on the spacetime coordinates in use. But the qualitative description of various phenomena can appear superficially quite different. Furthermore, we consider falling into a classical black hole using four distinct but equivalent metrics. First is the Schwarzschild case, with extreme time dilation at the horizon. Second, rescaling the dilation allows falling into the hole in finite proper time. Third, time and space are rescaled into a Penrose motivated picture where light trajectories all have unit slope. Fourth, a white hole variation of the second metric allows passage out through the horizon, with reentry forbidden.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Kleinian black holes

We prove there is a unique vacuum solution in split-signature spacetimes with Kleinian S O ( 2 , 1 ) spherical symmetry. We extend our analysis to accommodate a positive or negative cosmological constant and we prove the Kleinian spherically symmetric solutions to Einstein’s equation are locally isomorphic to the split-signature analogs of Schwarzschild–(anti)-de Sitter or Nariai spacetimes. Our analysis provides a Kleinian extension of Birkhoff’s theorem to metrics with split signature. Axisymmetric vacuum solutions are also considered, including (2,2) signature formulations of the Kerr and Taub-Newman-Unti-Tamburino metrics. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Equivalence principle in Reissner–Nordström geometry

The Equivalence Principle is a key element in the development of General Relativity. In one of its formulations, the Equivalence Principle states that a reference frame at rest in a uniform gravitational field is equivalent to a reference frame in uniformly accelerated motion in the absence of any gravitation field. We analyze the spacetime surrounding a non-rotating spherically symmetric charged body, known as Reissner–Nordström geometry, and exhibit a coordinate transformation, which makes explicit its compatibility with the Equivalence Principle. We revisit the Schwarzschild case, previously analyzed in the literature. We also consider second order terms of the relevant expansion parameters in the approximate metric, which is needed for the computed curvature quantities to be correct at zeroth order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Optical analogues to the equatorial Kerr–Newman black hole

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Convolutional double copy in (anti) de Sitter space

The double copy is a remarkable relationship between gauge theory and gravity that has been explored in a number of contexts, most notably scattering amplitudes and classical solutions. The convolutional double copy provides a straightforward method to bridge the two theories via a precise map for the fields and symmetries at the linearised level. This method has been thoroughly investigated in flat space, offering a comprehensive dictionary both with and without fixing the gauge degrees of freedom. In this paper, we extend this to curved space with an (anti) de Sitter background metric. We work in the temporal gauge, and employ a modified convolution that involves the Mellin transformation in the time direction. As an example, we show that the point-like charge in gauge theory double copies to the (dS-) Schwarzschild black hole solution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗