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Finite-Range Gravity and Its Role in Gravitational Waves, Black Holes and Cosmology

Stanislav V. Babak, L. P. Grishchuk

TL;DR

This work develops finite-range gravity as a two-parameter, field-theoretical modification of GR with explicit mass terms for the spin-2 and spin-0 gravitons, connected to parameters $\alpha^2$ and $\beta^2$ (via $\alpha^2=4k_1$, $\beta^2=-2k_1(k_1+4k_2)/(k_1+k_2)$) and masses $m_2=\alpha\hbar/c$, $m_0=\beta\hbar/c$. It demonstrates that GR is recovered in the massless limit and local weak-field tests are satisfied, but non-linear dynamics predict dramatic departures, notably the removal of black-hole horizons in static spherically symmetric spacetimes and oscillatory or accelerated cosmologies depending on the mass signs. The FP case ( $k_2=-k_1$ ) is shown to be inconsistent with static-field and gravitational-wave observations, while non-Fierz variants are free from negative-energy pathologies. The study combines exact non-linear equations with linear and weak-field analyses to reveal that arbitrarily small masses can drastically alter strong-field and cosmological behavior, potentially offering alternative explanations for horizon physics and cosmic acceleration, while remaining compatible with current experiments in the appropriate limits.

Abstract

Theoretical considerations of fundamental physics, as well as certain cosmological observations, persistently point out to permissibility, and maybe necessity, of macroscopic modifications of the Einstein general relativity. The field-theoretical formulation of general relativity helped us to identify the phenomenological seeds of such modifications. They take place in the form of very specific mass-terms, which appear in addition to the field-theoretical analog of the usual Hilbert-Einstein Lagrangian. We interpret the added terms as masses of the spin-2 and spin-0 gravitons. The arising finite-range gravity is a fully consistent theory, which smoothly approaches general relativity in the massless limit, that is, when both masses tend to zero and the range of gravity tends to infinity. We show that all local weak-field predictions of the theory are in perfect agreement with the available experimental data. However, some other conclusions of the non-linear massive theory are in a striking contrast with those of general relativity. We show in detail how the arbitrarily small mass-terms eliminate the black hole event horizon and replace a permanent power-law expansion of a homogeneous isotropic universe with an oscillatory behaviour. One variant of the theory allows the cosmological scale factor to exhibit an `accelerated expansion'instead of slowing down to a regular maximum of expansion. We show in detail why the traditional, Fierz-Pauli, massive gravity is in conflict not only with the static-field experiments but also with the available indirect gravitational-wave observations. At the same time, we demonstrate the incorrectness of the widely held belief that the non-Fierz-Pauli theories possess `negative energies' and `instabilities'.

Finite-Range Gravity and Its Role in Gravitational Waves, Black Holes and Cosmology

TL;DR

This work develops finite-range gravity as a two-parameter, field-theoretical modification of GR with explicit mass terms for the spin-2 and spin-0 gravitons, connected to parameters $\alpha^2$ and $\beta^2$ (via $\alpha^2=4k_1$, $\beta^2=-2k_1(k_1+4k_2)/(k_1+k_2)$) and masses $m_2=\alpha\hbar/c$, $m_0=\beta\hbar/c$. It demonstrates that GR is recovered in the massless limit and local weak-field tests are satisfied, but non-linear dynamics predict dramatic departures, notably the removal of black-hole horizons in static spherically symmetric spacetimes and oscillatory or accelerated cosmologies depending on the mass signs. The FP case ( $k_2=-k_1$ ) is shown to be inconsistent with static-field and gravitational-wave observations, while non-Fierz variants are free from negative-energy pathologies. The study combines exact non-linear equations with linear and weak-field analyses to reveal that arbitrarily small masses can drastically alter strong-field and cosmological behavior, potentially offering alternative explanations for horizon physics and cosmic acceleration, while remaining compatible with current experiments in the appropriate limits.

Abstract

Theoretical considerations of fundamental physics, as well as certain cosmological observations, persistently point out to permissibility, and maybe necessity, of macroscopic modifications of the Einstein general relativity. The field-theoretical formulation of general relativity helped us to identify the phenomenological seeds of such modifications. They take place in the form of very specific mass-terms, which appear in addition to the field-theoretical analog of the usual Hilbert-Einstein Lagrangian. We interpret the added terms as masses of the spin-2 and spin-0 gravitons. The arising finite-range gravity is a fully consistent theory, which smoothly approaches general relativity in the massless limit, that is, when both masses tend to zero and the range of gravity tends to infinity. We show that all local weak-field predictions of the theory are in perfect agreement with the available experimental data. However, some other conclusions of the non-linear massive theory are in a striking contrast with those of general relativity. We show in detail how the arbitrarily small mass-terms eliminate the black hole event horizon and replace a permanent power-law expansion of a homogeneous isotropic universe with an oscillatory behaviour. One variant of the theory allows the cosmological scale factor to exhibit an `accelerated expansion'instead of slowing down to a regular maximum of expansion. We show in detail why the traditional, Fierz-Pauli, massive gravity is in conflict not only with the static-field experiments but also with the available indirect gravitational-wave observations. At the same time, we demonstrate the incorrectness of the widely held belief that the non-Fierz-Pauli theories possess `negative energies' and `instabilities'.

Paper Structure

This paper contains 18 sections, 208 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Source-free gravitational field
  3. Gravitational field with matter sources
  4. Linearised theory of the source-free gravitational field
  5. Weak gravitational waves
  6. Weak gravitational waves in general relativity.
  7. Gravitational waves in the finite-range gravity.
  8. Observable manifestations of gravitational waves in the finite-range gravity.
  9. The Fierz-Pauli case.
  10. Black holes
  11. The general non-linear equations
  12. Weak-field approximation in the case $\zeta=1$
  13. No black holes in massive gravity
  14. Cosmology
  15. Homogeneous isotropic solutions in GR
  16. ...and 3 more sections

Figures (11)

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  • ...and 6 more figures