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Determination of varying speed of light from Black hole

Seokcheon Lee

TL;DR

The paper investigates whether a cosmological time evolution described by Generalized Cosmological Time (GCT/meVSL) with $b \simeq 0.04$ can coexist with stable local gravitational systems, specifically black holes. It employs geometric shielding, realized through Israel junction conditions, to join a locally static Schwarzschild interior to a time-dependent GCT-FLRW exterior with a lapse $N(t) \propto a^{b/4}$, resulting in a decoupled interior time gauge and a local effective parameter $b_{\mathrm{local}} \simeq 0$. Consequently, black hole thermodynamics reduces to the standard GR form and the Generalized Second Law (GSL) is satisfied without constraining the global background parameter $b$. The work thus shows that black hole stability provides a consistency requirement for geometric shielding rather than evidence for or against the underlying cosmological model, illustrating a viable separation between local and cosmological time normalizations within the GCT framework.

Abstract

The Generalized Cosmological Time (GCT) framework offers an alternative phenomenological approach to addressing the Hubble tension and the observed time dilation of Type Ia supernovae, characterized by a background parameter b \simeq 0.04 and an associated cosmological scaling of fundamental constants. A key conceptual question is whether such a background evolution is compatible with the stability of local, gravitationally bound systems, in particular black holes. This work examines black hole thermodynamics within the GCT framework, focusing on the geometric compatibility between a locally static region and a time-dependent cosmological background. By matching a static interior spacetime to a GCT-FLRW exterior across a timelike boundary, it is shown that the Israel junction conditions allow for the coexistence of distinct time normalizations without introducing surface stresses. In this setting, the local interior naturally admits a unit lapse function, while the background evolution is encoded in the cosmological time gauge. The resulting separation of time normalizations implies that the effective GCT parameter governing local physics is observationally indistinguishable from b_{\mathrm{local}} \simeq 0. Under this geometric shielding, black hole thermodynamics reduces to its standard general relativistic form, and the Generalized Second Law is satisfied without imposing additional constraints on the background parameter b. These results indicate that the empirical stability of black hole thermodynamics does not directly constrain the global GCT evolution but instead reflects a geometric decoupling between local and cosmological time gauges. Black hole stability thus emerges as a consistency condition for geometric shielding, rather than as independent evidence for or against the underlying cosmological model.

Determination of varying speed of light from Black hole

TL;DR

The paper investigates whether a cosmological time evolution described by Generalized Cosmological Time (GCT/meVSL) with can coexist with stable local gravitational systems, specifically black holes. It employs geometric shielding, realized through Israel junction conditions, to join a locally static Schwarzschild interior to a time-dependent GCT-FLRW exterior with a lapse , resulting in a decoupled interior time gauge and a local effective parameter . Consequently, black hole thermodynamics reduces to the standard GR form and the Generalized Second Law (GSL) is satisfied without constraining the global background parameter . The work thus shows that black hole stability provides a consistency requirement for geometric shielding rather than evidence for or against the underlying cosmological model, illustrating a viable separation between local and cosmological time normalizations within the GCT framework.

Abstract

The Generalized Cosmological Time (GCT) framework offers an alternative phenomenological approach to addressing the Hubble tension and the observed time dilation of Type Ia supernovae, characterized by a background parameter b \simeq 0.04 and an associated cosmological scaling of fundamental constants. A key conceptual question is whether such a background evolution is compatible with the stability of local, gravitationally bound systems, in particular black holes. This work examines black hole thermodynamics within the GCT framework, focusing on the geometric compatibility between a locally static region and a time-dependent cosmological background. By matching a static interior spacetime to a GCT-FLRW exterior across a timelike boundary, it is shown that the Israel junction conditions allow for the coexistence of distinct time normalizations without introducing surface stresses. In this setting, the local interior naturally admits a unit lapse function, while the background evolution is encoded in the cosmological time gauge. The resulting separation of time normalizations implies that the effective GCT parameter governing local physics is observationally indistinguishable from b_{\mathrm{local}} \simeq 0. Under this geometric shielding, black hole thermodynamics reduces to its standard general relativistic form, and the Generalized Second Law is satisfied without imposing additional constraints on the background parameter b. These results indicate that the empirical stability of black hole thermodynamics does not directly constrain the global GCT evolution but instead reflects a geometric decoupling between local and cosmological time gauges. Black hole stability thus emerges as a consistency condition for geometric shielding, rather than as independent evidence for or against the underlying cosmological model.

Paper Structure

This paper contains 10 sections, 39 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Geometric Shielding via Metric Junction
  3. Robustness of Black Hole Thermodynamics
  4. Conclusion
  5. Basics of BH
  6. Entropy of BH system
  7. $\tilde{T}_{\text{BH}} > T_{\text{env}}$
  8. $dQ_{\text{H}}/dt = 0$ ( i.e., $k_{\text{B}} T_{\text{BH}} \leq m_{e} c^2$)
  9. $dQ_{\text{H}}/dt \neq 0$ ( i.e., $k_{\text{B}} T_{\text{BH}} \geq m_{e} c^2$)
  10. $\tilde{T}_{\text{BH}} \leq T_{\text{env}}$

Figures (1)

  • Figure 1: The behaviors of different definitions of BH charges as a function of BH mass. The solid, dotted, dashed, and dot-dashed lines represent $Q_{\text{Max}} \,, Q_{e} \,, Q_{\text{bp}}$ , and $Q_{\text{pp}}$, respectively. a) The behaviors of them for the mass range up to $4 \times 10^{-16} M_{\odot}$. b) Their behaviors for the mass range to $6 \times 10^{5} M_{\odot}$.