.. _sphx_glr_api_gallery_relativity_kerr:

Kerr black holes
-----------------

Frame dragging, the ergosphere, and the Penrose process.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A rotating (Kerr) black hole of mass M and spin parameter a = J/M \in [0, M), found by Roy Kerr in 1963, drags spacetime itself around with it. Outside the horizon r_+ = M + \sqrt{M^2-a^2}, in the ergosphere">

.. only:: html

  .. image:: /api/gallery/relativity/kerr/images/thumb/sphx_glr_plot_ergosphere_and_penrose_thumb.png
    :alt:

  :doc:`/api/gallery/relativity/kerr/plot_ergosphere_and_penrose`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Frame dragging and the ergosphere of a Kerr black hole</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A rotating black hole&#x27;s shadow is not a perfect circle like Schwarzschild&#x27;s: frame dragging shifts and flattens it along the direction of rotation, and the accretion disk&#x27;s approaching side is Doppler-boosted bright while the receding side dims -- exactly the asymmetric brightness pattern seen in the 2019 Event Horizon Telescope image of M87*. This example ray-traces the full (non-equatorial) Kerr null geodesic equations -- using Carter&#x27;s separated equations of motion in Mino time -- to render the shadow of a black hole of mass M and spin parameter a at increasing spin, and shades a thin, circularly orbiting equatorial accretion disk by its combined gravitational and Doppler redshift">

.. only:: html

  .. image:: /api/gallery/relativity/kerr/images/thumb/sphx_glr_plot_kerr_shadow_and_redshift_thumb.png
    :alt:

  :doc:`/api/gallery/relativity/kerr/plot_kerr_shadow_and_redshift`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Kerr shadow: a rotating black hole's asymmetric silhouette</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Roger Penrose realized in 1969 that the ergosphere of a rotating (Kerr) black hole -- see plot_ergosphere_and_penrose -- is not just a region where no observer can sit still, but a genuine energy resource. Inside it, the t-Killing vector associated with time-translation symmetry becomes spacelike, so a particle there can have negative energy as measured by an observer at infinity. If a particle entering the ergosphere splits in two, with one negative-energy fragment falling into the horizon, energy conservation forces the escaping fragment to carry away more energy than the original particle had -- extracting rotational energy from the black hole itself. The process is capped by Hawking&#x27;s area theorem: the hole&#x27;s irreducible mass can never decrease, limiting the maximum extractable fraction to">

.. only:: html

  .. image:: /api/gallery/relativity/kerr/images/thumb/sphx_glr_plot_penrose_energy_extraction_thumb.png
    :alt:

  :doc:`/api/gallery/relativity/kerr/plot_penrose_energy_extraction`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Penrose process: extracting a black hole's rotational energy</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The static, side-by-side spin comparison in plot_kerr_shadow_and_redshift already shows that a black hole&#x27;s shadow shrinks and its accretion disk creeps inward as the spin a increases -- but a continuous sweep makes the mechanism far more vivid: watch the innermost stable circular orbit (ISCO) contract from 6M (Schwarzschild) down toward M (extremal Kerr, prograde), dragging the disk&#x27;s bright inner edge inward with it, while the shadow itself flattens and shifts off-center from frame dragging.">

.. only:: html

  .. image:: /api/gallery/relativity/kerr/images/thumb/sphx_glr_plot_shadow_spin_sweep_animation_thumb.gif
    :alt:

  :doc:`/api/gallery/relativity/kerr/plot_shadow_spin_sweep_animation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Animating the shadow: a black hole spun up from rest</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/relativity/kerr/plot_ergosphere_and_penrose
   /api/gallery/relativity/kerr/plot_kerr_shadow_and_redshift
   /api/gallery/relativity/kerr/plot_penrose_energy_extraction
   /api/gallery/relativity/kerr/plot_shadow_spin_sweep_animation