Gravity’s Link to Thermodynamics Extends Beyond Standard Space-Time, Research Confirms

Scientists are re-examining the foundations of classical gravity through the lens of thermodynamics, building upon Ted Jacobson’s groundbreaking work which demonstrated that Einstein’s field equations emerge from the first law of thermodynamics applied to a Rindler horizon. Jhan N. Martinez (Escuela de Física, Universidad Industrial de Santander), Jose F. Rodriguez-Ruiz (Departamento de Física, Universidad Antonio Nariño) and Yeinzon Rodriguez (Centro de Investigaciones en Ciencias Básicas y Aplicadas, Universidad Antonio Nariño and Escuela de Física, Universidad Industrial de Santander) et al. now extend this thermodynamic approach to explore non-Riemannian geometries, investigating the implications of torsion and non-metricity. This research is significant because it challenges the prevailing assumption that the Einstein-Hilbert action represents the simplest, and therefore most likely, gravitational theory, instead suggesting a modified theory incorporating torsion may better describe gravity in more general geometric frameworks.

Thermodynamic origins of gravity in non-Riemannian spacetime geometries are increasingly explored

Scientists are re-evaluating fundamental assumptions about gravity following a new analysis of thermodynamic principles and non-Riemannian geometries. This work builds upon a surprising proposal from three decades ago, suggesting that gravitational field equations may arise from the laws of thermodynamics as observed by a specific type of observer.
Researchers have now extended this concept to geometries beyond the standard Riemannian framework, those incorporating torsion and non-metricity, revealing unexpected constraints on possible gravitational theories. The study demonstrates that the commonly accepted Einstein-Hilbert action, considered the simplest gravitational theory, is not generally viable in these non-Riemannian scenarios, except when restricted to Riemannian geometry.

This investigation began with the question of whether Nature had a genuine choice when establishing the laws governing gravity. By applying thermodynamic principles to spacetime, specifically the first law, the team explored the implications for the underlying affine and metric structures of the universe.

Their analysis reveals a limited set of viable options, narrowing the possibilities for gravitational theories beyond General Relativity. The approach differs from standard methods of constructing gravitational theories, instead deriving them from thermodynamic equations of state.

This strategy, rooted in the behaviour of black hole horizons and the principles of entropy, offers a novel perspective on the foundations of gravity. However, the researchers found that this consistent pathway breaks down when considering fully non-Riemannian geometries, highlighting a fundamental incompatibility between the two approaches under these conditions.

The findings suggest that General Relativity, while effective, may not be the ultimate description of gravity, but rather an emergent phenomenon arising from underlying thermodynamic principles. This perspective aligns with the idea that GR represents an equation of state for spacetime, valid under specific conditions of local equilibrium. The work opens avenues for exploring more fundamental theories of gravity, potentially bridging the gap between classical physics and the quantum realm, and may offer insights into the nature of spacetime itself.

Thermodynamic implications of non-Riemannian spacetime geometries for gravitational theories remain a challenging area of research

Researchers began by examining the implications of thermodynamics on affine and metric structures within spacetime manifolds, considering both Riemannian and non-Riemannian geometries. The study specifically investigated how relaxing the assumption of a symmetric, metric-compatible connection, the standard approach in constructing General Relativity, would affect gravitational theories.

This involved analysing the consequences of the first law of thermodynamics applied locally to Rindler observers, mirroring the approach initially proposed by Ted Jacobson three decades prior. The work builds upon the established connection between gravity, thermodynamics, and black hole dynamics, extending it to geometries incorporating torsion and non-metricity.

To establish a framework for evaluating potential gravitational theories, the research employed the area law of entropy, postulating a direct proportionality between changes in entropy and horizon area, expressed as δS ∝ δA. This principle, combined with the Clausius relation (δQ = TδS), was used to derive gravitational field equations as thermodynamic equations of state, identifying energy flux as δQ and the Unruh temperature as T.

Crucially, the imposition of local energy-momentum conservation served to uniquely reduce this family of equations to the Einstein field equations of General Relativity within the Riemannian case. The study differentiated between scenarios with asymmetric connections (characterised by Torsion) and those with incompatible connections (characterised by Non-Metricity), revealing that the gravitational theory derived from the Einstein-Hilbert action, augmented with a quadratic term in the torsion vector, emerges as a likely candidate in the non-Riemannian case lacking non-metricity. However, this strategy proved inconsistent when considering fully non-Riemannian geometries, highlighting a fundamental divergence in the theoretical landscape.

Thermodynamic selection of torsion-based gravity in non-Riemannian spacetime offers a compelling alternative to general relativity

Researchers investigating the foundations of gravity have identified a specific gravitational theory favoured by thermodynamic principles in non-Riemannian spacetime. Analysis reveals that a gravitational theory derived from the Einstein-Hilbert action, augmented with a term quadratic in the torsion vector, emerges as the preferred model when considering geometries involving torsion but not non-metricity.

This selection process stems from applying the first law of thermodynamics to Rindler observers and examining the resulting gravitational field equations. The work builds upon Jacobson’s earlier proposal that gravitational field equations arise from thermodynamic considerations, specifically the area law of entropy and the Clausius relation.

By extending this approach to non-Riemannian geometries, the study explores alternatives to the standard Einstein-Hilbert action, which is typically favoured in Riemannian spacetime. However, this convergence breaks down when considering fully non-Riemannian geometries, where the two approaches yield mutually inconsistent results.

The research highlights a potential thermodynamic basis for selecting gravitational laws, suggesting that General Relativity may be an equation of state rather than a fundamental description of gravity. This thermodynamic derivation relies on the area law of entropy, where changes in horizon area are proportional to changes in entropy, and the Clausius relation linking heat exchange to temperature and entropy.

Identifying energy flux as heat exchange and the Unruh temperature as temperature, researchers derived a family of gravitational field equations. Imposing local energy-momentum conservation uniquely selects the Einstein field equations within the Riemannian framework, but this constraint does not hold in non-Riemannian scenarios, leading to the identified torsion-based alternative.

Emergent gravity in modified geometric frameworks and constraints on non-Riemannian theories offer promising avenues for quantum gravity research

Scientists have investigated the foundations of gravity by extending Jacobson’s approach, linking gravity to thermodynamics, to non-Riemannian geometries incorporating torsion and non-metricity. Their work reveals that the standard Einstein-Hilbert action, typically considered a fundamental basis for gravitational theories, is not a viable option in these more general geometric frameworks, except when restricted to Riemannian spacetime.

By applying principles from both Jacobson’s work and the Lanczos-Lovelock theories, researchers identified a unique gravitational theory for non-Riemannian spacetimes lacking non-metricity, one derived from the Einstein-Hilbert action augmented with a term proportional to the square of the torsion vector. Further analysis demonstrated an incompatibility between the requirements of both approaches when non-metricity is fully considered, indicating a conflict in formulating a consistent theory under these conditions.

As a secondary outcome, the investigation pinpointed new terms related to non-metricity that potentially contribute to the Hartle-Hawking tidal heating observed around black holes, offering a possible avenue for detecting torsion and non-metricity through observational astronomy. This research establishes that, without the constraints of Riemannian geometry, the simplest gravitational theory requires modification, specifically the inclusion of a torsion-dependent term, to align with thermodynamic principles and the Lanczos-Lovelock framework.

The authors acknowledge a limitation in their analysis, namely the assumption of four-dimensional spacetime, and note that exploring higher dimensions could yield different results. Future research may focus on investigating the observational consequences of the identified non-metricity terms in black hole physics, potentially providing empirical evidence for torsion and non-metricity in the universe, or on resolving the inconsistencies that arise when incorporating both torsion and non-metricity into a unified gravitational theory.