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  2. 6. Black Holes Black holes are among the most ...

    www.damtp.cam.ac.uk/user/tong/gr/six.pdf
    31 May 2024: our old coordinates, we’re instead going to find a new set of coordinates that works. ... everywhere. Our first step is to introduce a new radial coordinate, r?, defined by.

  3. 3. Introducing Riemannian Geometry We have yet to meet ...

    www.damtp.cam.ac.uk/user/tong/gr/three.pdf
    31 May 2024: Z). = fR(!; X, Y, Z). Thus, both torsion and curvature define new tensors on our manifold. – ... change of coordinates to xµ(x̃) which does the trick. In the new coordinates,.

  4. Preprint typeset in JHEP style - HYPER VERSION Michaelmas ...

    www.damtp.cam.ac.uk/user/tong/gr/one.pdf
    31 May 2024: generate. a new solution. • Reparameterisation invariance: We introduced as an arbitrary parameterisationof the path. ... Then we could equally as well construct an action S̃ using this new parameter,.

  5. 4. The Einstein Equations It is now time to ...

    www.damtp.cam.ac.uk/user/tong/gr/four.pdf
    31 May 2024: M, we can usethis to map all fields, including the metric, on M to a new set of fields on M.

  6. Vector Calculus University of Cambridge Part IA Mathematical Tripos…

    www.damtp.cam.ac.uk/user/tong/vc/vc.pdf
    12 Jun 2024: For. such curves, we introduce new notation and write the line integral asC. ... should be viewed as infinitesimally close to each other. These two new segments have.

  7. G-Adaptive mesh refinement - leveraging graphneural networks and…

    www.damtp.cam.ac.uk/user/gam37/preprints/preprint_g-adaptive_mesh_refinement.pdf
    11 Jun 2024: Our new approach combines agraph neural network (GNN) powered architecture, with training based on directminimisation of the FE solution error with respect to the mesh point locations. ... Contributions Indeed, our central novelty is to provide a new

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