Master’s Thesis Title

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Galaxy clusters assemble hierarchically through mergers whose shocks, turbulence, and core disruption leave rich thermal (X-ray) and non-thermal (radio) imprints. Inferring the underlying merger parameters—time since/to pericenter, collision velocity, mass ratio, pericenter distance, and component masses—is scientifically valuable but much of the relevant information is lost or distorted in observations. Moreover, observations provide only single-epoch snapshots rather than time-resolved tracks over Gyr, so reliable ground-truth labels are scarce. Hence we use TNG–Cluster simulations and its 352 zoom-in halos in three orthogonal projections across 0 ≤ z ≤ 1 to create intrinsic maps and their merger parameters. Building on these data, this thesis develops an end-to-end, simulation-based route from images to calibrated posteriors over merger physics. First, SimCLR encoder, a contrastive learning framework, are trained separately for X-ray, radio, and for paired X-ray+radio maps to learn morphology-aware representation that distill high-resolution maps into feature vectors that capture the relevant structure. A physics-aware augmentation suite (rotations, flips, Gaussian blur, additive noise, and affine zoom/shift; applied channel-consistently in the joint case) promotes invariance to observing nuisances without erasing merger signatures. Second, a conditional invertible neural network (cINN) with rational–quadratic spline couplings and a mixture-of-experts partition in representation space enabling inference of the p(x|c), where x is the merger parameter and c is the conditioner. Two conditioning modes are evaluated: (i) representation-conditioned, where c is the learned embedding (X-ray, radio, or joint); and (ii) scalar-conditioned, where c is a vector of scalar observable parameters that are fed directly to the cINN, without contrastive learning.

Across four conditioners schemes; scalars, X-ray embedding, radio embedding, and joint X-ray+radio, the method is evaluated on both last- and next-merger targets. Radio conditioning delivers the sharpest and best-calibrated posteriors, with typical MAP ranges of collision time ∼[−5, 10]%, velocity ≤ ±1%, main cluster's M_500c, subcluster mass ∼ ±0.5%, and pericenter distance ∼ ±3%, reflecting the close coupling of radio emission and its geometry to recent cluster dynamics. X-ray conditioning remains informative, but produces broader posteriors and larger scatter in MAP estimates. Joint conditioning is consistently intermediate: it narrows and stabilizes inferences relative to X-ray alone, but it does not surpass radio conditioning. Scalar conditioning on the other hand, performs competitively only for collision time and the main cluster mass, while elsewhere it is not calibrated and suffers from heteroscedastic dispersions, pointing to the information bottle neck that could be introduced by only using scalar parameters. In all cases, the cINN not only recovers ΛCDM-consistent cross-parameter correlations, but also uses the learned correlations encoded in the joint density to propagate information from well constrained coordinated to weaker ones. Forecasts for the next merger mirror last-merger performance with modest, physically expected broadening (most visible for timing). Methodologically, this thesis demonstrates that label-free contrastive representation used directly as cINN condition enable survey-scale, uncertainty-aware inference of cluster assembly from imaging alone. Practically, the results argue for prioritizing high-fidelity radio imaging. In future research, this framework can be extended toward instrument-aware mock observables for sim-to-real transfer, multi-resolution fusion including SZ and weak-lensing, and scalable pipelines suitable for eROSITA/Chandra/XMM paired with LOFAR/MeerKAT/VLA.

Black Hole Information Paradox

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In this project, we studied the paradox of black hole information and a few possible solutions that have been suggested. We began with a brief look at the history of black holes and the introduction to some of the useful mathematical tools for studying them and then moved on to the similarities between the laws of classical and black holes’ thermodynamics. In the next chapter, we obtained Hawking radiation using the Unruh effect, and the reason for using this method was to demonstrate the dependence of the concepts of particles and vacuum on the observer. Next, information and its relationship with entropy were introduced. In the last section, we discussed the leading cause of the paradox, which is the vacuum without information in the event horizon predicted by general relativity. As the black holes evaporate, this vacuum stretches to produce a Hawking pair.

The first solution was the idea of remnants; a relatively old idea that the evaporation of a black hole will stop when it reaches Planck size. Following that, we analyzed Page’s average information and proved it mathematically. Moreover, we looked at Page’s theory which suggests that the information starts to come out only after the black hole has reached its Page time. Finally, we studied the complementarity theory and the interesting article on entanglement and wormholes. The proposed solutions each had contradictions: infinite malice in the remnant theory, loss of information in Page theory, and the existence of a firewall at the black hole’s event horizon in the complementarity approach, which conflicts with general relativity’s equivalence principle.