It's not correct to say that GR and QM are incompatible (or compatible)-that's a meaningless statement.

The AdS/CFT correspondence (introduced by Maldacena in 1997) is a postulate (in the general case) and states that gravity, in an AdS spacetime, in d spacetime dimensions, is dual to a non-gravitational field theory, with conformal symmetry on its-flat-boundary, which has d-1 spacetime dimensions. One implication of this postulate is that classical gravity in an AdS spacetime, in d dimensions, is dual to a conformal quantum field theory-at strong coupling-in d-1 dimensions. Another implication is that, in a theory of quantum gravity, in which this correspondence would hold, there exist quantities that are invariant under the flow of the gravitational coupling. It is this implication that is relevant for identifying what are called black hole microstates and using them to identify the states that describe the entropy of black holes-which are classical objects-when probed by known quantum matter, if one has a theory that claims to do that. This is what became possible in string theory in the 1990s, starting with the work of Strominger and Vafa, in fact, which predates the proposal of the AdS/CFT correspondence itself.

It is this calculation, that is under control, that shows that the notion of black hole entropy (introduced by Christodoulou and elaborated, in particular, by Bekenstein and Hawking) makes sense, in particular, admits a statisical mechanical interpretation-at least for a certain class of black holes (the so-called ``extremal'' black holes).

Whether Hawking radiation is well-defined is, still, not completely understood. The reason is that it, still, isn't possible to compute it beyond the semi-classical approximation. The experiments that claim to measure it in fluids , in fact measure something completely different, since the ``analog'' black hole spacetimes don't have singularities.

While the pre-inflationary epoch of the universe is, indeed, the realm of quantum gravity, it's, still, not possible to, either do experiments, or set up calculations that make any sense in that context.

Bottom line: The problem of quantum gravity is, from the theoretical side, finding a quantum theory, whose classical limit is general relativity, a gauge theory with noncompact gauge group and, from the experimental side, setting up experiments that can probe the pre-inflationary epoch of the universe. How to do either is an open problem.

there are significant theoretical developments where these two pillars of physics intersect, by way of high level summary

1. Theoretical Link — The Maldacena AdS/CFT Correspondence (1997)

Juan Maldacena introduced the AdS/CFT correspondence in 1997, not 1988. This conjecture proposes a duality between a type of string theory formulated in a higher-dimensional Anti-de Sitter (AdS) space and a Conformal Field Theory (CFT) without gravity on its boundary. Essentially, it suggests that a gravitational theory in AdS space can be equivalent to a quantum field theory in one fewer dimension.

• Significance

The AdS/CFT correspondence is considered by many as one of the most important developments in theoretical physics for linking GR and QM. It provides a mathematical framework where problems in quantum gravity can be translated into problems in quantum field theory, and vice versa.

• Wider Engagement

The conjecture has garnered extensive research interest and has been a fertile ground for theoretical exploration. It has deepened our understanding of black holes, quantum entanglement, and strongly coupled quantum systems.

• Limitations

Despite its theoretical elegance, the AdS/CFT correspondence remains a conjecture. It applies specifically to universes with AdS geometry, which does not describe our observed universe’s de Sitter (dS) geometry. Therefore, it hasn’t yet led to experimentally testable predictions or a complete unification of GR and QM.

2. Hawking Radiation — Theoretical Prediction Awaiting Experimental Verification

Stephen Hawking’s prediction of black hole radiation in 1974 is a seminal contribution that combines principles from both GR and QM.

• Concept

Hawking radiation arises from quantum effects near a black hole’s event horizon. Virtual particle-antiparticle pairs near the horizon can result in one particle escaping as radiation while the other falls into the black hole, leading to a gradual loss of mass.

• Significance

This phenomenon suggests that black holes are not entirely black but emit radiation, linking quantum field theory with the curved spacetime of GR.

• Experimental Status

Direct detection of Hawking radiation from astrophysical black holes is currently beyond our technological capabilities due to its incredibly weak signal. However, analogue systems in laboratories have simulated aspects of Hawking radiation, but these are not direct observations of the phenomenon.

3. Planck Time and Early Universe Theorisation

The Planck time (~ seconds) represents a scale where quantum gravitational effects cannot be ignored.

• Early Universe Models

Theorising about the universe at times earlier than the Planck time requires a quantum theory of gravity. Models like loop quantum gravity and string theory attempt to describe this epoch.

• Testable Predictions

While these theories are mathematically robust, they currently lack experimentally testable predictions. Advancements in observational cosmology or high-energy physics may provide avenues for testing these ideas in the future.

maybe…

• Significance

Understanding physics at the Planck scale is crucial for a complete picture of cosmology and could illuminate the unification of GR and QM.

so, what does it all mean ?

While a full reconciliation between General Relativity and Quantum Mechanics remains one of the foremost challenges in physics, these points of intersection provide some good direction.

The Maldacena AdS/CFT correspondence offers a powerful theoretical tool, Hawking radiation bridges concepts from both theories, and exploring the Planck era pushes the boundaries of our understanding.

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