Does a page table itself have a virtual address?

Question

If not, how does the kernel build a page table when creating a new process, and modify a page table entry when swapping in/out a page of a process?

I think that instructions, running in either user mode or kernel mode, can only use a virtual address (which is then converted to a physical address by the CPU internal hardware) to access anywhere in the RAM (and memory-mapping peripherals), unless MMU is disabled.

I know that the kernel is responsible for creating and maintaining page tables while the CPU's internal hardware logic looks up in the page table(CR3 in x86 stores the base address of the page table of the current process, which is a physical address) to convert a virtual address to a physical address.

My question is: when the instructions in the kernel code that try to modify the content of a page table entry are executing, how is the virtual address (if any) of the page table itself converted to a physical address? Must MMU be disabled during that time so that no address-translation is needed?

Answer 1

These should answer your question:
JamesM's kernel development tutorials (read the explanation under "6.4.2. Required definitions")
Paging - OSDev Wiki (read section 6 Manipulation)

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Original half-baked answer:

The physical address of the current page directory¹ is stored in the CPU register CR3.

Virtual address translation is dictated by the kernel, there is no cryptic internal hardware in the CPU.

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Direct quote from Virtual and Physical Addresses - University of Waterloo

Dynamic Relocation

• The memory management unit (MMU) of the CPU contains a relocation register.
• Whenever a thread tries to access a memory location (through a virtual address), the value of the relocation register is added to the virtual memory address – dynamic binding.
• The kernel maintains a separate relocation value¹ for each process (as part of the virtual address space); changes the relocation register at every context switch.