Research Atlas

Choose a direction by finding a question you care about, a method you can learn to use well, and a first result you can check. The Research Atlas connects eight fields and 48 research questions to concrete starting projects, the evidence behind them, and the obstacles that matter. Use this page to make a shortlist; use a field guide to compare projects; use a question page to plan a reproduction and a possible extension. The scientific assessments retain their stated 2026-08-20 evidence cutoff. The project suggestions are starting points, not claims that an extension is still unexplored.

Find a direction that fits your way of working

Begin with the work you want to do day to day. Most research crosses these categories, but choosing a primary method makes the first project easier to scope.

• Prove a precise statement. Start with mathematical and global relativity. You should enjoy reconstructing estimates, checking hypotheses, and understanding why a proof fails just outside its domain. Repair gaps with analysis for mathematical relativity.
• Calculate how a black hole or binary responds. Compare black-hole stability and dynamics with binaries and radiation. A useful entry capability is deriving a perturbation equation and checking a numerical solution against a controlled limit. The black-hole perturbation path develops that preparation.
• Extract a physical conclusion from data. Compare observation and astrophysics with tests of gravity. You need to enjoy likelihoods, selection effects, and testing whether another model explains the same result. Use the probability and inference bridge if those tools are unfamiliar.
• Connect the early universe to observable signals. Start with cosmology and primordial black holes. Your first project may be a transfer-function calculation, an abundance calculation, or a constraint recast; these require different preparation. The relativistic cosmology path helps distinguish them.
• Understand quantum states, entropy, and spacetime. Compare semiclassical gravity and information with quantum gravity and holography. Choose whether your immediate tool is quantum field theory, quantum information, or a microscopic model. Start with the QFT in curved spacetime path or quantum-information bridge as appropriate.

If you are still learning the Einstein equation, geodesics, horizons, and perturbation theory, use the graduate GR path alongside one narrow research question. Reading a frontier paper can motivate preparation; understanding its abstract is not yet the capability to extend its result.

Compare the eight research fields

These examples describe possible first outputs, not unsolved problems with guaranteed solutions. Each field guide supplies specific readings and projects. Omission from the 48 questions is not a judgment of scientific importance.

Field	A useful first output	Main constraint to discuss
Mathematical and global relativity	A reconstructed estimate with explicit hypotheses	Analysis preparation and proof supervision
Black-hole stability and dynamics	A checked reduced model or instability diagnostic	Whether the reduction retains the relevant dynamics
Binaries and radiation	An invariant comparison or controlled waveform experiment	Common conventions and independent errors
Observation and astrophysics	A release-specific sensitivity or selection study	Access to the inputs needed to rerun inference
Tests and beyond GR	A model-specific consistency or degeneracy calculation	Theory validity and the observable mapping
Cosmology and primordial black holes	A transfer-function or constraint calculation	Assumptions linking early- and late-time physics
Semiclassical gravity and information	A controlled entropy or stress-tensor calculation	State, subsystem, renormalization, and backreaction
Quantum gravity and holography	A worked result in one microscopic model	A precise dictionary and controlled approximation

Turn a broad interest into a finite question

A direction names a subject; a project names a result you could show someone. Write the proposed result before extending the reading list. These examples illustrate the change in scale:

• “Black-hole spectroscopy” → In a specified synthetic ringdown with a fixed noise model, how does an inferred second component change as the fitting start time moves? Begin with overtone identifiability; a better fit alone does not identify an overtone.
• “Cosmic censorship” → Which regularity assumption prevents continuation in one stated theorem, and what changes in the relevant estimate if it is weakened? Begin with strong cosmic censorship and regularity; a calculation in a symmetric model does not settle generic evolution.
• “Black holes as dark matter” → How does one published constraint change when its monochromatic mass assumption is replaced by a specified extended distribution, where that recasting prescription applies? Begin with PBH constraint synthesis; do not combine incompatible likelihoods or read an allowed interval as evidence for PBHs.
• “The information problem” → Which subsystem and approximation produce an entropy transition in one solvable model, and which proposed extension would leave that approximation? Begin with island calculations; reproducing the transition is a learning result, not a solution of generic evaporation.

These are bounded formulations. Their potential research value depends on what has already been done and whether the change addresses a consequential uncertainty. A smaller, well-checked question can be the right starting point for an ambitious long-term direction.

Test the choice with a short pilot

Agree a limited pilot with a supervisor or collaborator before committing a thesis chapter. A four- to six-week pilot can be a useful planning window when the prerequisites are already in place; allow more preparation when they are not. The checkpoints matter more than the calendar.

1. Formulate and read. Select one question page. Read its linked background, then the primary source for the starting result and the strongest adverse or limiting result. Write down the observable or theorem, assumptions, boundary conditions, and exact disagreement. The output is a one-page formulation that an expert can correct.
2. Reproduce the baseline. Re-derive one equation or lemma, regenerate one diagnostic, or inspect one released inference product. Record the source version and your own choices. A copied plot is not a reproduction; numerical agreement requires a stated quantity, error measure, and refinement check. The output is an inspectable calculation or argument.
3. Change one assumption. Try one controlled variation while keeping a comparison with the baseline. Separate a real effect from a gauge choice, convention mismatch, prior choice, resolution error, or missing input. The output can be a failed reproduction or a demonstrated degeneracy if the failure is understood.
4. Decide whether to continue. Present the result, remaining uncertainty, and next experiment or lemma. Continue if the baseline works, the proposed gap survives a literature search, and the next test is feasible. Narrow or change direction if the required data are inaccessible, the approximation fails where the effect occurs, or the main dependency has no credible route to resolution.

When reproduction fails, debug the setup before interpreting the disagreement as new physics. When the extension gives a null result, ask whether the calculation had enough sensitivity to exclude the effect you proposed. Both outcomes can improve a project; neither automatically makes a publishable contribution.

Match the project to resources and supervision

A laptop is enough for many analytic checks, small numerical experiments, and inspections of released data products. It is not a resource estimate for a full numerical-relativity campaign or a high-dimensional inference run. Measure the runtime and memory of the smallest representative calculation, then estimate the number of parameter points, resolutions, noise realizations, and independent checks required. For a proof project, a crucial resource is someone who can diagnose a failed estimate and distinguish a technical gap from a false proposition.

Bring two candidate projects to a prospective supervisor. Ask which part they can supervise directly, who can check the other method, what data or computing access is available, and how often you will discuss intermediate results. Ask for an example of a suitably scoped first project in the group. A famous open problem is not a substitute for this support; a working local collaboration can make an otherwise difficult project practical.

For researchers moving between fields, start with the assumptions that fail to transfer. Determine whether two papers use the same observable, asymptotic conditions, subsystem, dataset, or notion of error before planning a synthesis. The research seminar guide provides a structured way to present and challenge such comparisons.

Check novelty and write a one-page proposal

Search the exact observable, theorem hypotheses, model, and approximation order—not only the broad topic name. Follow both the references of the baseline paper and later papers citing it; inspect revised versions, corrections, and released code or data. ADS, INSPIRE, and the source links on each record provide entry points. Keep a short comparison of the nearest results: what they compute, where they apply, and what your proposed calculation would add. A missing phrase in a search result is not a novelty check. Search beyond the record’s evidence cutoff before treating any suggested extension as open.

Use these prompts after the pilot to expose dependencies early:

• Question: What finite statement, measurement, or comparison will the project decide, and in what domain?
• Motivation: Which uncertainty matters, and to whom would resolving it be useful?
• Baseline: Which exact result will be reproduced, with what inputs and validation?
• Proposed contribution: What changes, and which nearest papers establish that this is a meaningful gap?
• Resources and support: Which skills, data, software, compute, and expert feedback are available?
• Deliverables and alternatives: What will exist at the next checkpoint, what would count as a useful negative result, and what observation would make you stop or narrow the project?

A viable proposal need not promise a discovery. It should make the next decision possible. If every deliverable depends on solving the entire frontier problem first, reduce the scope until there is an intermediate result worth checking.

How to read an assessment

A frontier question rarely has one honest one-word answer. A theorem can settle a restricted model while the broader physical question remains open; an observation can strongly constrain one parameterization without supporting the underlying theory; a numerical result can be converged but nongeneric. Read each assessment by asking three questions: what is settled, what supports the conclusion, and how reliable is that interpretation?

Axis	What it tells you	What it does not tell you
Question status	Whether the finite question is open, partially resolved, resolved, or refuted	How strong or reliable the evidence is
Evidence status	Whether the evidence is established, supported, contested, speculative, or insufficient	Whether all broader versions of the question have the same answer
Confidence	How reliable this assessment is, given source quality, independence, and scope	A numerical posterior probability unless one is explicitly supplied

Read the domain row before the conclusion. “Supported” for a symmetry-reduced theorem, a BPS sector, or a named detector catalogue is not a claim about generic four-dimensional dynamics. When different subdomains have different answers, the comparison table treats them separately.

How evidence is weighted

Evidence types are compared by what they can establish. A proof controls precisely its hypotheses and conclusion. A numerical evolution also needs equations, initial and boundary data, constraint and convergence tests, and a failure boundary. An observational result needs a pinned release and calibration, selection function, forward model, likelihood or estimator, priors, nuisance model, and systematic-error treatment. A lower-dimensional model or toy calculation can demonstrate a mechanism, but it does not inherit authority over four-dimensional gravity merely because the mechanism is suggestive.

Independence matters as much as quantity. Three papers using the same data, waveform family, simulation code, or unproved analytic input are not three independent confirmations. Conversely, a credible adverse result is not hidden because it applies in a neighboring domain: the record explains whether it refutes the proposition, narrows its domain, or only defeats one method. A null search counts as evidence only over the sensitivity region it actually covered.

Dates and what could change a conclusion

Each assessment states the date through which it considers results. A later catalogue, calibration, corrected preprint, proof, counterexample, failed reproduction, or improved simulation may change the conclusion. The “What could change the conclusion” row identifies a result that could resolve an uncertainty or overturn an interpretation.

The cutoff does not indicate consensus or a probability of completing your project. It tells you which later results you need to look for before relying on the assessment. A question can remain open even when the available results have been examined carefully. Changes to a suggested project do not extend the scientific cutoff.